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In this paper we propose a rate-distortion optimal algorithm for sinusoidal coding of audio and speech. The algorithm determines for a pre-specified target bit-rate the optimal (variable-length) time segmentation, the optimal distribution of sinusoidal components over the segments and the optimal (scalar) quantisers for quantising the sinusoid parameters amplitude, phase and frequency. The optimisation is done by jointly optimising the segment lengths, number of sinusoids and quantisers using high-resolution quantisation theory and dynamic programming techniques, which makes it possible to execute the algorithm in polynomial time. A particular advantage of the proposed method is that, given a target bit-rate, it solves the problem of finding the optimal balance between total number of sinusoids and number of bits per sinusoid.